The homotopy category of cotorsion flat quasi-coherent sheaves over quasi-compact and quasi-separated schemes

Document Type : Original Paper

Author

Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

Let X be a quasi-compact and semi-separated scheme and QcoX be the category of all quasi-coherent sheaves of O_X -modules. We show that any flat complex of cotorsion quasi-coherent sheaves of O_X -modules is contractible. As an application, it is shown that the homotopy category of cotorsion flat quasi-coherent sheaves of O_X -modules is the natural replacement of the homotopy category of projectives.

Highlights

1.J. Asadollahi and S.h. Salarian (2012). Cohomology theories based on
flats, J. Algebra, 353 (1), 93-120.
2.E. Enochs and J.R. Garcıa Rozas ́
 (1998). Flat covers of complexes, J.
Algebra, 0 (1), 86-102.
3. E. Enochs and S. Estrada (2005). Relative homological algebra in the
category of quasi-coherent sheaves, Adv. Math. 194 (2), 284-295.
4. R. Hartshorne (1997). Algebraic Geometry, Springer-Verlag.
5.E. Hosseini (2019). The pure derived categories of quasi-coherent
sheaves, Comm Algebra, 47(9), 3781-3788.

Keywords

Main Subjects

References

1.J. Asadollahi and S.h. Salarian (2012). Cohomology theories based on
flats, J. Algebra, 353 (1), 93-120.
2.E. Enochs and J.R. Garcıa Rozas ́
 (1998). Flat covers of complexes, J.
Algebra, 0 (1), 86-102.
3. E. Enochs and S. Estrada (2005). Relative homological algebra in the
category of quasi-coherent sheaves, Adv. Math. 194 (2), 284-295.
4. R. Hartshorne (1997). Algebraic Geometry, Springer-Verlag.
5.E. Hosseini (2019). The pure derived categories of quasi-coherent
sheaves, Comm Algebra, 47(9), 3781-3788.
Journal of Advanced Mathematical Modeling
Volume 10, Issue 2
December 2020
Pages 341-355

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History

  • Receive Date: 08 July 2019
  • Revise Date: 20 April 2020
  • Accept Date: 23 May 2020

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